diff options
| -rw-r--r-- | DESCRIPTION | 9 | ||||
| -rw-r--r-- | NAMESPACE | 2 | ||||
| -rw-r--r-- | R/tranche_functions.R | 879 | ||||
| -rw-r--r-- | src/Makevars | 2 | ||||
| -rw-r--r-- | src/Makevars.win | 2 | ||||
| -rw-r--r-- | src/lossdistrib.c | 760 | ||||
| -rw-r--r-- | src/lossdistrib.h | 46 |
7 files changed, 1700 insertions, 0 deletions
diff --git a/DESCRIPTION b/DESCRIPTION new file mode 100644 index 0000000..166cebd --- /dev/null +++ b/DESCRIPTION @@ -0,0 +1,9 @@ +Package: lossdistrib +Type: Package +Title: What the package does (short line) +Version: 1.0 +Date: 2014-04-24 +Author: Who wrote it +Maintainer: Who to complain to <yourfault@somewhere.net> +Description: More about what it does (maybe more than one line) +License: What license is it under? diff --git a/NAMESPACE b/NAMESPACE new file mode 100644 index 0000000..f2e6748 --- /dev/null +++ b/NAMESPACE @@ -0,0 +1,2 @@ +exportPattern("^[[:alpha:]]+") +useDynLib("lossdistrib") diff --git a/R/tranche_functions.R b/R/tranche_functions.R new file mode 100644 index 0000000..2e7f0f3 --- /dev/null +++ b/R/tranche_functions.R @@ -0,0 +1,879 @@ +library(statmod)
+
+## todo:
+## -investigate other ways to interpolate the random severities on the grid
+## I'm thinking that at eah severity that we add to the distribution, round it down
+## and keep track of the missing mass: namely if X_i=S_i w.p p_i, then add
+## X_i=lu*floor(S_i/lu) with probability p_i and propagate
+## X_{i+1}=S_{i+1}+(S_i-lu*floor(S_i/lu)) with the right probability
+## - investigate truncated distributions more (need to compute loss and recov distribution
+## separately, for the 0-10 equity tranche, we need the loss on the 0-0.1 support and
+## recovery with 0.1-1 support, so it's not clear that there is a big gain.
+## - do the correlation adjustments when computing the deltas since it seems to be
+## the market standard
+hostname <- system("hostname", intern=TRUE)
+
+checkSymbol <- function(name){
+ if(!is.loaded(name)){
+ if(.Platform$OS.type == "unix"){
+ root.dir <- "/home/share/CorpCDOs"
+ dyn.load(file.path(root.dir, "code", "R", paste0("lossdistrib",
+ hostname,
+ .Platform$dynlib.ext)))
+ }else{
+ root.dir <- "//WDSENTINEL/share/CorpCDOs"
+ dyn.load(file.path(root.dir, "code", "R", paste0("lossdistrib",
+ .Platform$dynlib.ext)))
+ }
+ }
+}
+lossdistrib <- function(p){
+ ## basic recursive algorithm of Andersen, Sidenius and Basu
+ n <- length(p)
+ q <- rep(0, (n+1))
+ q[1] <- 1
+ for(i in 1:n){
+ q[-1] <- p[i]*q[-(n+1)]+(1-p[i])*q[-1]
+ q[1] <- (1-p[i])*q[1]
+ }
+ return(q)
+}
+
+lossdistrib.fft <- function(p){
+ ## computes loss distribution using the fft
+ ## complexity is of order O(n*m)+O(m*log(m))
+ ## where m is the size of the grid and n the number of probabilities.
+ ## this is slower than the recursive algorithm
+ theta <- 2*pi*1i*(0:n)/(n+1)
+ Phi <- 1 - p + p%o%exp(theta)
+ v <- apply(Phi, 2, prod)
+ return(1/(n+1)*Re(fft(v)))
+}
+
+lossdistrib2 <- function(p, w, S, N, defaultflag=FALSE){
+ ## recursive algorithm with first order correction
+ ## p vector of default probabilities
+ ## w vector of weigths
+ ## S vector of severities
+ ## N number of ticks in the grid
+ ## defaultflag if true computes the default distribution
+ n <- length(p)
+ lu <- 1/(N-1)
+ q <- rep(0, N)
+ q[1] <- 1
+ for(i in 1:n){
+ if(defaultflag){
+ d <- w[i] /lu
+ }else{
+ d <- S[i] * w[i] / lu
+ }
+ d1 <- floor(d)
+ d2 <- ceiling(d)
+ p1 <- p[i]*(d2-d)
+ p2 <- p[i] - p1
+ q1 <- c(rep(0,d1), p1*q[1:(N-d1)])
+ q2 <- c(rep(0,d2), p2*q[1:(N-d2)])
+ q <- q1 + q2 + (1-p[i])*q
+ }
+ q[length(q)] <- q[length(q)]+1-sum(q)
+ return(q)
+}
+
+lossdistrib2.truncated <- function(p, w, S, N, cutoff=N){
+ ## recursive algorithm with first order correction
+ ## p vector of default probabilities
+ ## w vector of weigths
+ ## S vector of severities
+ ## N number of ticks in the grid (for best accuracy should
+ ## be a multiple of the number of issuers)
+ ## cutoff where to stop computing the exact probabilities
+ ## (useful for tranche computations)
+
+ ## this is actually slower than lossdistrib2. But in C this is
+ ## twice as fast.
+ ## for high severities, M can become bigger than N, and there is
+ ## some probability mass escaping.
+ n <- length(p)
+ lu <- 1/(N-1)
+ q <- rep(0, truncated)
+ q[1] <- 1
+ M <- 1
+ for(i in 1:n){
+ d <- S[i] * w[i] / lu
+ d1 <- floor(d)
+ d2 <- ceiling(d)
+ p1 <- p[i]*(d2-d)
+ p2 <- p[i] - p1
+ q1 <- p1*q[1:min(M, cutoff-d1)]
+ q2 <- p2*q[1:min(M, cutoff-d2)]
+ q[1:min(M, cutoff)] <- (1-p[i])*q[1:min(M, cutoff)]
+ q[(d1+1):min(M+d1, cutoff)] <- q[(d1+1):min(M+d1, cutoff)]+q1
+ q[(d2+1):min(M+d2, cutoff)] <- q[(d2+1):min(M+d2, cutoff)]+q2
+ M <- M+d2
+ }
+ return(q)
+}
+
+recovdist <- function(dp, pp, w, S, N){
+ ## computes the recovery distribution for a sum of independent variables
+ ## R=\sum_{i=1}^n X_i
+ ## where X_i = 0 w.p 1-dp[i]-pp[i]
+ ## = w[i]*(1-S[i]) w.p dp[i]
+ ## = w[i] w.p pp[i]
+ ## each non zero value v is interpolated on the grid as
+ ## the pair of values floor(v/lu) and ceiling(v/lu) so that
+ ## X_i has four non zero values
+ n <- length(dp)
+ q <- rep(0, N)
+ q[1] <- 1
+ lu <- 1/(N-1)
+ for(i in 1:n){
+ d1 <- w[i]*(1-S[i])/lu
+ d1l <- floor(d1)
+ d1u <- ceiling(d1)
+ d2 <- w[i] / lu
+ d2l <- floor(d2)
+ d2u <- ceiling(d2)
+ dp1 <- dp[i] * (d1u-d1)
+ dp2 <- dp[i] - dp1
+ pp1 <- pp[i] * (d2u - d2)
+ pp2 <- pp[i] - pp1
+ q1 <- c(rep(0, d1l), dp1 * q[1:(N-d1l)])
+ q2 <- c(rep(0, d1u), dp2 * q[1:(N-d1u)])
+ q3 <- c(rep(0, d2l), pp1 * q[1:(N-d2l)])
+ q4 <- c(rep(0, d2u), pp2 *q[1:(N-d2u)])
+ q <- q1+q2+q3+q4+(1-dp[i]-pp[i])*q
+ }
+ return(q)
+}
+
+lossdist.joint <- function(p, w, S, N, defaultflag=FALSE){
+ ## recursive algorithm with first order correction
+ ## to compute the joint probability distribution of the loss and recovery
+ ## inputs:
+ ## p: vector of default probabilities
+ ## w: vector of issuer weights
+ ## S: vector of severities
+ ## N: number of tick sizes on the grid
+ ## defaultflag: if true computes the default distribution
+ ## output:
+ ## q: matrix of joint loss, recovery probability
+ ## colSums(q) is the recovery distribution marginal
+ ## rowSums(q) is the loss distribution marginal
+ n <- length(p)
+ lu <- 1/(N-1)
+ q <- matrix(0, N, N)
+ q[1,1] <- 1
+ for(k in 1:n){
+ if(defaultflag){
+ x <- w[k] / lu
+ }else{
+ x <- S[k] * w[k]/lu
+ }
+ y <- (1-S[k]) * w[k]/lu
+ i <- floor(x)
+ j <- floor(y)
+ weights <- c((i+1-x)*(j+1-y), (i+1-x)*(y-j), (x-i)*(y-j), (j+1-y)*(x-i))
+ psplit <- p[k] * weights
+ qtemp <- matrix(0, N, N)
+ qtemp[(i+1):N,(j+1):N] <- qtemp[(i+1):N,(j+1):N] + psplit[1] * q[1:(N-i),1:(N-j)]
+ qtemp[(i+1):N,(j+2):N] <- qtemp[(i+1):N,(j+2):N] + psplit[2] * q[1:(N-i), 1:(N-j-1)]
+ qtemp[(i+2):N,(j+2):N] <- qtemp[(i+2):N,(j+2):N] + psplit[3] * q[1:(N-i-1), 1:(N-j-1)]
+ qtemp[(i+2):N, (j+1):N] <- qtemp[(i+2):N, (j+1):N] + psplit[4] * q[1:(N-i-1), 1:(N-j)]
+ q <- qtemp + (1-p[k])*q
+ }
+ q[length(q)] <- q[length(q)]+1-sum(q)
+ return(q)
+}
+
+lossdist.prepay.joint <- function(dp, pp, w, S, N, defaultflag=FALSE){
+ ## recursive algorithm with first order correction
+ ## to compute the joint probability distribition of the loss and recovery
+ ## inputs:
+ ## dp: vector of default probabilities
+ ## pp: vector of prepay probabilities
+ ## w: vector of issuer weights
+ ## S: vector of severities
+ ## N: number of tick sizes on the grid
+ ## defaultflag: if true computes the default
+ ## outputs
+ ## q: matrix of joint loss and recovery probability
+ ## colSums(q) is the recovery distribution marginal
+ ## rowSums(q) is the loss distribution marginal
+ n <- length(dp)
+ lu <- 1/(N-1)
+ q <- matrix(0, N, N)
+ q[1,1] <- 1
+ for(k in 1:n){
+ y1 <- (1-S[k]) * w[k]/lu
+ y2 <- w[k]/lu
+ j1 <- floor(y1)
+ j2 <- floor(y2)
+ if(defaultflag){
+ x <- y2
+ i <- j2
+ }else{
+ x <- y2-y1
+ i <- floor(x)
+ }
+
+ ## weights <- c((i+1-x)*(j1+1-y1), (i+1-x)*(y1-j1), (x-i)*(y1-j1), (j1+1-y1)*(x-i))
+ weights1 <- c((i+1-x)*(j1+1-y1), (i+1-x)*(y1-j1), (x-i)*(y1-j1), (j1+1-y1)*(x-i))
+ dpsplit <- dp[k] * weights1
+
+ if(defaultflag){
+ weights2 <- c((i+1-x)*(j2+1-y2), (i+1-x)*(y2-j2), (x-i)*(y2-j2), (j2+1-y2)*(x-i))
+ ppsplit <- pp[k] * weights2
+ }else{
+ ppsplit <- pp[k] * c(j2+1-y2, y2-j2)
+ }
+ qtemp <- matrix(0, N, N)
+ qtemp[(i+1):N,(j1+1):N] <- qtemp[(i+1):N,(j1+1):N] + dpsplit[1] * q[1:(N-i),1:(N-j1)]
+ qtemp[(i+1):N,(j1+2):N] <- qtemp[(i+1):N,(j1+2):N] + dpsplit[2] * q[1:(N-i), 1:(N-j1-1)]
+ qtemp[(i+2):N,(j1+2):N] <- qtemp[(i+2):N,(j1+2):N] + dpsplit[3] * q[1:(N-i-1), 1:(N-j1-1)]
+ qtemp[(i+2):N,(j1+1):N] <- qtemp[(i+2):N, (j1+1):N] + dpsplit[4] * q[1:(N-i-1), 1:(N-j1)]
+ if(defaultflag){
+ qtemp[(i+1):N,(j2+1):N] <- qtemp[(i+1):N,(j2+1):N] + ppsplit[1] * q[1:(N-i),1:(N-j2)]
+ qtemp[(i+1):N,(j2+2):N] <- qtemp[(i+1):N,(j2+2):N] + ppsplit[2] * q[1:(N-i), 1:(N-j2-1)]
+ qtemp[(i+2):N,(j2+2):N] <- qtemp[(i+2):N,(j2+2):N] + ppsplit[3] * q[1:(N-i-1), 1:(N-j2-1)]
+ qtemp[(i+2):N,(j2+1):N] <- qtemp[(i+2):N, (j2+1):N] + ppsplit[4] * q[1:(N-i-1), 1:(N-j2)]
+ }else{
+ qtemp[, (j2+1):N] <- qtemp[,(j2+1):N]+ppsplit[1]*q[,1:(N-j2)]
+ qtemp[, (j2+2):N] <- qtemp[,(j2+2):N]+ppsplit[2]*q[,1:(N-j2-1)]
+ }
+ q <- qtemp + (1-pp[k]-dp[k]) * q
+ }
+ q[length(q)] <- q[length(q)] + 1 - sum(q)
+ return(q)
+}
+
+lossdistC <- function(p, w, S, N, defaultflag=FALSE){
+ ## C version of lossdistrib2, roughly 50 times faster
+ .C("lossdistrib", as.double(p), as.integer(length(p)),
+ as.double(w), as.double(S), as.integer(N), as.logical(defaultflag), q = double(N))$q
+}
+
+lossdistCblas <- function(p, w, S, N, defaultflag=FALSE){
+ ## C version of lossdistrib2, roughly 50 times faster
+ .C("lossdistrib_blas", as.double(p), as.integer(length(p)),
+ as.double(w), as.double(S), as.integer(N), as.logical(defaultflag), q = double(N))$q
+}
+
+lossdistCZ <- function(p, w, S, N, defaultflag=FALSE, rho, Z, wZ){
+ .C("lossdistrib_Z", as.double(p), as.integer(length(p)),
+ as.double(w), as.double(S), as.integer(N), as.logical(defaultflag),
+ as.double(rho), as.double(Z), as.integer(length(Z)),
+ q = matrix(0, N, length(Z)))$q
+}
+
+lossdistC.truncated <- function(p, w, S, N, T=N){
+ ## C version of lossdistrib2, roughly 50 times faster
+ .C("lossdistrib_truncated", as.double(p), as.integer(length(p)),
+ as.double(w), as.double(S), as.integer(N), as.integer(T), q = double(T))$q
+}
+
+recovdistC <- function(dp, pp, w, S, N){
+ ## C version of recovdist
+ .C("recovdist", as.double(dp), as.double(pp), as.integer(length(dp)),
+ as.double(w), as.double(S), as.integer(N), q = double(N))$q
+}
+
+lossdistC.joint <- function(p, w, S, N, defaultflag=FALSE){
+ ## C version of lossdistrib.joint, roughly 20 times faster
+ .C("lossdistrib_joint", as.double(p), as.integer(length(p)), as.double(w),
+ as.double(S), as.integer(N), as.logical(defaultflag), q = matrix(0, N, N))$q
+}
+
+lossdistC.jointblas <- function(p, w, S, N, defaultflag=FALSE){
+ ## C version of lossdistrib.joint, roughly 20 times faster
+ .C("lossdistrib_joint_blas", as.double(p), as.integer(length(p)), as.double(w),
+ as.double(S), as.integer(N), as.logical(defaultflag), q = matrix(0, N, N))$q
+}
+
+
+lossdistC.jointZ <- function(dp, w, S, N, defaultflag = FALSE, rho, Z, wZ){
+ ## N is the size of the grid
+ ## dp is of size n.credits
+ ## w is of size n.credits
+ ## S is of size n.credits by nZ
+ ## rho is a double
+ ## Z is a vector of length nZ
+ ## w is a vector if length wZ
+ r <- .C("lossdistrib_joint_Z", as.double(dp), as.integer(length(dp)),
+ as.double(w), as.double(S), as.integer(N), as.logical(defaultflag), as.double(rho),
+ as.double(Z), as.double(wZ), as.integer(length(Z)), q = matrix(0, N, N))$q
+}
+
+lossdistC.prepay.joint <- function(dp, pp, w, S, N, defaultflag=FALSE){
+ ## C version of lossdist.prepay.joint
+ r <- .C("lossdistrib_prepay_joint", as.double(dp), as.double(pp), as.integer(length(dp)),
+ as.double(w), as.double(S), as.integer(N), as.logical(defaultflag), q=matrix(0, N, N))$q
+ return(r)
+}
+
+lossdistC.prepay.jointZ <- function(dp, pp, w, S, N, defaultflag = FALSE, rho, Z, wZ){
+ ## N is the size of the grid
+ ## dp is of size n.credits
+ ## pp is of size n.credits
+ ## w is of size n.credits
+ ## S is of size n.credits by nZ
+ ## rho is a double
+ ## Z is a vector of length nZ
+ ## w is a vector if length wZ
+ r <- .C("lossdistrib_prepay_joint_Z", as.double(dp), as.double(pp), as.integer(length(dp)),
+ as.double(w), as.double(S), as.integer(N), as.logical(defaultflag), as.double(rho),
+ as.double(Z), as.double(wZ), as.integer(length(Z)), q = matrix(0, N, N))$q
+}
+
+lossrecovdist <- function(defaultprob, prepayprob, w, S, N, defaultflag=FALSE, useC=TRUE){
+ if(missing(prepayprob)){
+ if(useC){
+ L <- lossdistC(defaultprob, w, S, N, defaultflag)
+ R <- lossdistC(defaultprob, w, 1-S, N)
+ }else{
+ L <- lossdistrib2(defaultprob, w, S, N, defaultflag)
+ R <- lossdistrib2(defaultprob, w, 1-S, N)
+ }
+ }else{
+ if(useC){
+ L <- lossdistC(defaultprob+defaultflag*prepayprob, w, S, N, defaultflag)
+ R <- recovdistC(defaultprob, prepayprob, w, S, N)
+ }else{
+ L <- lossdistrib2(defaultprob+defaultflag*prepayprob, w, S, N, defaultflag)
+ R <- recovdist(defaultprob, prepayprob, w, S, N)
+ }
+ }
+ return(list(L=L, R=R))
+}
+
+lossrecovdist.term <- function(defaultprob, prepayprob, w, S, N, defaultflag=FALSE, useC=TRUE){
+ ## computes the loss and recovery distribution over time
+ L <- array(0, dim=c(N, ncol(defaultprob)))
+ R <- array(0, dim=c(N, ncol(defaultprob)))
+ if(missing(prepayprob)){
+ for(t in 1:ncol(defaultprob)){
+ temp <- lossrecovdist(defaultprob[,t], , w, S[,t], N, defaultflag, useC)
+ L[,t] <- temp$L
+ R[,t] <- temp$R
+ }
+ }else{
+ for(t in 1:ncol(defaultprob)){
+ temp <- lossrecovdist(defaultprob[,t], prepayprob[,t], w, S[,t], N, defaultflag, useC)
+ L[,t] <- temp$L
+ R[,t] <- temp$R
+ }
+ }
+ return(list(L=L, R=R))
+}
+
+lossrecovdist.joint.term <- function(defaultprob, prepayprob, w, S, N, defaultflag=FALSE, useC=TRUE){
+ ## computes the joint loss and recovery distribution over time
+ Q <- array(0, dim=c(ncol(defaultprob), N, N))
+ if(useC){
+ if(missing(prepayprob)){
+ for(t in 1:ncol(defaultprob)){
+ Q[t,,] <- lossdistC.joint(defaultprob[,t], w, S[,t], N, defaultflag)
+ }
+ }else{
+ for(t in 1:ncol(defaultprob)){
+ Q[t,,] <- lossdistC.prepay.joint(defaultprob[,t], prepayprob[,t], w, S[,t], N, defaultflag)
+ }
+ }
+ }else{
+ if(missing(prepayprob)){
+ for(t in 1:ncol(defaultprob)){
+ Q[t,,] <- lossdist.joint(defaultprob[,t], w, S[,t], N, defaultflag)
+ }
+ }else{
+ for(t in 1:ncol(defaultprob)){
+ Q[t,,] <- lossdist.prepay.joint(defaultprob[,t], prepayprob[,t], w, S[,t], N, defaultflag)
+ }
+ }
+ }
+ gc()
+ return(Q)
+}
+
+dist.transform <- function(dist.joint){
+ ## compute the joint (D, R) distribution
+ ## from the (L, R) distribution using D = L+R
+ distDR <- array(0, dim=dim(dist.joint))
+ Ngrid <- dim(dist.joint)[2]
+ for(t in 1:dim(dist.joint)[1]){
+ for(i in 1:Ngrid){
+ for(j in 1:Ngrid){
+ index <- i+j
+ if(index <= Ngrid){
+ distDR[t,index,j] <- distDR[t,index,j] + dist.joint[t,i,j]
+ }else{
+ distDR[t,Ngrid,j] <- distDR[t,Ngrid,j] +
+ dist.joint[t,i,j]
+ }
+ }
+ }
+ distDR[t,,] <- distDR[t,,]/sum(distDR[t,,])
+ }
+ return( distDR )
+}
+
+shockprob <- function(p, rho, Z, log.p=F){
+ ## computes the shocked default probability as a function of the copula factor
+ ## function is vectorized provided the below caveats:
+ ## p and rho are vectors of same length n, Z is a scalar, returns vector of length n
+ ## p and rho are scalars, Z is a vector of length n, returns vector of length n
+ if(length(p)==1){
+ if(rho==1){
+ return(Z<=qnorm(p))
+ }else{
+ return(pnorm((qnorm(p)-sqrt(rho)*Z)/sqrt(1-rho), log.p=log.p))
+ }
+ }else{
+ result <- double(length(p))
+ result[rho==1] <- Z<=qnorm(p[rho==1])
+ result[rho<1] <- pnorm((qnorm(p[rho<1])-sqrt(rho[rho<1])*Z)/sqrt(1-rho[rho<1]), log.p=log.p)
+ return( result )
+ }
+}
+
+shockseverity <- function(S, Stilde=1, Z, rho, p){
+ ## computes the severity as a function of the copula factor Z
+ result <- double(length(S))
+ result[p==0] <- 0
+ result[p!=0] <- Stilde * exp( shockprob(S[p!=0]/Stilde*p[p!=0], rho[p!=0], Z, TRUE) -
+ shockprob(p[p!=0], rho[p!=0], Z, TRUE))
+ return(result)
+}
+
+dshockprob <- function(p,rho,Z){
+ dnorm((qnorm(p)-sqrt(rho)*Z)/sqrt(1-rho))*dqnorm(p)/sqrt(1-rho)
+}
+
+dqnorm <- function(x){
+ 1/dnorm(qnorm(x))
+}
+
+fit.prob <- function(Z, w, rho, p0){
+ ## if the weights are not perfectly gaussian, find the probability p such
+ ## E_w(shockprob(p, rho, Z)) = p0
+ require(distr)
+ if(p0==0){
+ return(0)
+ }
+ if(rho == 1){
+ distw <- DiscreteDistribution(Z, w)
+ return(pnorm(q(distw)(p0)))
+ }
+ eps <- 1e-12
+ dp <- (crossprod(shockprob(p0,rho,Z),w)-p0)/crossprod(dshockprob(p0,rho,Z),w)
+ p <- p0
+ while(abs(dp) > eps){
+ dp <- (crossprod(shockprob(p,rho,Z),w)-p0)/crossprod(dshockprob(p,rho,Z),w)
+ phi <- 1
+ while ((p-phi*dp)<0 || (p-phi*dp)>1){
+ phi <- 0.8*phi
+ }
+ p <- p - phi*dp
+ }
+ return(p)
+}
+
+fit.probC <- function(Z, w, rho, p0){
+ r <- .C("fitprob", as.double(Z), as.double(w), as.integer(length(Z)),
+ as.double(rho), as.double(p0), q = double(1))
+ return(r$q)
+}
+
+stochasticrecov <- function(R, Rtilde, Z, w, rho, porig, pmod){
+ ## if porig == 0 (probably matured asset) then return orginal recovery
+ ## it shouldn't matter anyway since we never default that asset
+ if(porig == 0){
+ return(rep(R, length(Z)))
+ }else{
+ ptilde <- fit.prob(Z, w, rho, (1-R)/(1-Rtilde) * porig)
+ return(abs(1-(1-Rtilde) * exp(shockprob(ptilde, rho, Z, TRUE) - shockprob(pmod, rho, Z, TRUE))))
+ }
+}
+
+stochasticrecovC <- function(R, Rtilde, Z, w, rho, porig, pmod){
+ r <- .C("stochasticrecov", as.double(R), as.double(Rtilde), as.double(Z),
+ as.double(w), as.integer(length(Z)), as.double(rho), as.double(porig),
+ as.double(pmod), q = double(length(Z)))
+ return(r$q)
+}
+
+pos <- function(x){
+ pmax(x, 0)
+}
+
+trancheloss <- function(L, K1, K2){
+ pos(L - K1) - pos(L - K2)
+}
+
+trancherecov <- function(R, K1, K2){
+ pos(R - 1 + K2) - pos(R - 1 +K1)
+}
+
+tranche.cl <- function(L, R, cs, K1, K2, Ngrid=nrow(L), scaled=FALSE){
+ ## computes the couponleg of a tranche
+ ## if scaled is TRUE, scale it by the size of the tranche (K2-K1)
+ ## can make use of the fact that the loss and recov distribution are
+ ## truncated (in that case nrow(L) != Ngrid
+ if(K1==K2){
+ return( 0 )
+ }else{
+ support <- seq(0, 1, length=Ngrid)[1:nrow(L)]
+ size <- K2 - K1 - crossprod(trancheloss(support, K1, K2), L) -
+ crossprod(trancherecov(support, K1, K2), R)
+ sizeadj <- as.numeric(0.5 * (size + c(K2-K1, size[-length(size)])))
+ if(scaled){
+ return( 1/(K2-K1) * crossprod(sizeadj * cs$coupons, cs$df) )
+ }else{
+ return( crossprod(sizeadj * cs$coupons, cs$df) )
+ }
+ }
+}
+
+tranche.cl.scenarios <- function(l, r, cs, K1, K2, scaled=FALSE){
+ ## computes the couponleg of a tranche for one scenario
+ ## if scaled is TRUE, scale it by the size of the tranche (K2-K1)
+ ## can make use of the fact that the loss and recov distribution are
+ ## truncated (in that case nrow(L) != Ngrid
+ if(K1==K2){
+ return( 0 )
+ }else{
+ size <- K2 - K1 - trancheloss(l, K1, K2) - trancherecov(r, K1, K2)
+ sizeadj <- as.numeric(0.5 * (size + c(K2-K1, size[-length(size)])))
+ if(scaled){
+ return( 1/(K2-K1) * crossprod(sizeadj * cs$coupons, cs$df) )
+ }else{
+ return( crossprod(sizeadj * cs$coupons, cs$df) )
+ }
+ }
+}
+
+funded.tranche.pv <- function(L, R, cs, K1, K2, scaled = FALSE){
+ if(K1==K2){
+ return(0)
+ }else{
+ size <- K2 - K1 -trancheloss(L, K1, K2) - trancherecov(R, K1, K2)
+ sizeadj <- as.numeric(0.5 * (size + c(K2-K1, size[-length(size)])))
+ interest <- crossprod(sizeadj * cs$coupons, cs$df)
+ principal <- diff(c(0, trancherecov(R, K1, K2)))
+ principal[length(principal)] <- principal[length(principal)] + size[length(size)]
+ principal <- crossprod(cs$df, principal)
+ if(scaled){
+ pv <- (interest + principal)/(K2-K1)
+ }else{
+ pv <- (interest + principal)
+ }
+ return(pv)
+ }
+}
+
+tranche.pl <- function(L, cs, K1, K2, Ngrid=nrow(L), scaled=FALSE){
+ ## computes the protection leg of a tranche
+ ## if scaled
+ if(K1==K2){
+ return(0)
+ }else{
+ support <- seq(0, 1, length=Ngrid)[1:nrow(L)]
+ cf <- K2 - K1 - crossprod(trancheloss(support, K1, K2), L)
+ cf <- c(K2 - K1, cf)
+ if(scaled){
+ return( 1/(K2-K1) * crossprod(diff(cf), cs$df))
+ }else{
+ return( crossprod(diff(cf), cs$df))
+ }
+ }
+}
+
+tranche.pl.scenarios <- function(l, cs, K1, K2, scaled=FALSE){
+ ## computes the protection leg of a tranche
+ ## if scaled
+ if(K1==K2){
+ return(0)
+ }else{
+ cf <- K2 - K1 - trancheloss(l, K1, K2)
+ cf <- c(K2 - K1, cf)
+ if(scaled){
+ return( 1/(K2-K1) * as.numeric(crossprod(diff(cf), cs$df)))
+ }else{
+ return( as.numeric(crossprod(diff(cf), cs$df)))
+ }
+ }
+}
+
+tranche.pv <- function(L, R, cs, K1, K2, Ngrid=nrow(L)){
+ return( tranche.pl(L, cs, K1, K2, Ngrid) + tranche.cl(L, R, cs, K1, K2, Ngrid))
+}
+
+tranche.pv.scenarios <- function(l, r, cs, K1, K2){
+ return( tranche.pl.scenarios(l, cs, K1, K2, TRUE) +
+ tranche.cl.scenarios(l, r, cs, K1, K2, TRUE))
+}
+
+
+adjust.attachments <- function(K, losstodate, factor){
+ ## computes the attachments adjusted for losses
+ ## on current notional
+ return( pmin(pmax((K-losstodate)/factor, 0),1) )
+}
+
+tranche.pvvec <- function(K, L, R, cs){
+ r <- rep(0, length(K)-1)
+ for(i in 1:(length(K)-1)){
+ r[i] <- 1/(K[i+1]-K[i]) * tranche.pv(L, R, cs, K[i], K[i+1])
+ }
+ return( r )
+}
+
+BClossdist <- function(defaultprob, issuerweights, recov, rho, Z, w,
+ N=length(recov)+1, defaultflag=FALSE, n.int=500){
+ if(missing(Z)){
+ quadrature <- gauss.quad.prob(n.int, "normal")
+ Z <- quadrature$nodes
+ w <- quadrature$weights
+ }
+ ## do not use if weights are not gaussian, results would be incorrect
+ ## since shockseverity is invalid in that case (need to use stochasticrecov)
+ LZ <- matrix(0, N, length(Z))
+ RZ <- matrix(0, N, length(Z))
+ L <- matrix(0, N, ncol(defaultprob))
+ R <- matrix(0, N, ncol(defaultprob))
+ for(t in 1:ncol(defaultprob)){
+ for(i in 1:length(Z)){
+ g.shocked <- shockprob(defaultprob[,t], rho, Z[i])
+ S.shocked <- shockseverity(1-recov, 1, Z[i], rho, defaultprob[,t])
+ temp <- lossrecovdist(g.shocked, , issuerweights, S.shocked, N)
+ LZ[,i] <- temp$L
+ RZ[,i] <- temp$R
+ }
+ L[,t] <- LZ%*%w
+ R[,t] <- RZ%*%w
+ }
+ list(L=L, R=R)
+}
+
+BClossdistC <- function(defaultprob, issuerweights, recov, rho, Z, w,
+ N=length(issuerweights)+1, defaultflag=FALSE){
+ L <- matrix(0, N, dim(defaultprob)[2])
+ R <- matrix(0, N, dim(defaultprob)[2])
+ rho <- rep(rho, length(issuerweights))
+ r <- .C("BClossdist", defaultprob, dim(defaultprob)[1], dim(defaultprob)[2],
+ as.double(issuerweights), as.double(recov), as.double(Z), as.double(w),
+ as.integer(length(Z)), as.double(rho), as.integer(N), as.logical(defaultflag), L=L, R=R)
+ return(list(L=r$L,R=r$R))
+}
+
+BCtranche.pv <- function(defaultprob, issuerweights, recov, cs, K1, K2, rho1, rho2,
+ Z, w, N=length(issuerweights)+1){
+ ## computes the protection leg, couponleg, and bond price of a tranche
+ ## in the base correlation setting
+ if(K1==0){
+ if(rho1!=0){
+ stop("equity tranche must have 0 lower correlation")
+ }
+ }
+ dK <- K2 - K1
+ dist2 <- BClossdistC(defaultprob, issuerweights, recov, rho2, Z, w, N)
+ if(rho1!=0){
+ dist1 <- BClossdistC(defaultprob, issuerweights, recov, rho1, Z, w, N)
+ }
+ cl2 <- tranche.cl(dist2$L, dist2$R, cs, 0, K2)
+ cl1 <- tranche.cl(dist1$L, dist1$R, cs, 0, K1)
+ pl2 <- tranche.pl(dist2$L, cs, 0, K2)
+ pl1 <- tranche.pl(dist1$L, cs, 0, K1)
+ return(list(pl=(pl2-pl1)/dK, cl=(cl2-cl1)/dK,
+ bp=100*(1+(pl2-pl1+cl2-cl1)/dK)))
+}
+
+BCtranche.delta <- function(portfolio, index, coupon, K1, K2, rho1, rho2, Z, w,
+ N=length(portolio)+1, tradedate = Sys.Date()){
+ ## computes the tranche delta (on current notional) by doing a proportional
+ ## blip of all the curves
+ ## if K2==1, then computes the delta using the lower attachment only
+ ## this makes sense for bottom-up skews
+ eps <- 1e-4
+ portfolioplus <- portfolio
+ portfoliominus <- portfolio
+ cs <- couponSchedule(IMMDate(tradedate), index$maturity,"Q", "FIXED", coupon, 0, tradedate,
+ IMMDate(tradedate, "prev"))
+ for(i in 1:length(portfolio)){
+ portfolioplus[[i]]@curve@hazardrates <- portfolioplus[[i]]@curve@hazardrates * (1 + eps)
+ portfoliominus[[i]]@curve@hazardrates <- portfoliominus[[i]]@curve@hazardrates * (1- eps)
+ }
+ dPVindex <- indexpv(portfolioplus, index, tradedate = tradedate, clean = FALSE)$bp -
+ indexpv(portfoliominus, index, tradedate = tradedate, clean = FALSE)$bp
+ defaultprobplus <- 1 - SPmatrix(portfolioplus, length(cs$dates))
+ defaultprobminus <- 1 - SPmatrix(portfoliominus, length(cs$dates))
+ if(K2==1){
+ K1adj <- adjust.attachments(K1, index$loss, index$factor)
+ dPVtranche <- BCtranche.pv(defaultprobplus, issuerweights, recov, cs, 0, K1adj, 0, rho1,
+ Z, w, N)$bp -
+ BCtranche.pv(defaultprobminus, issuerweights, recov, cs, 0, K1adj, 0, rho1,
+ Z, w, N)$bp
+ delta <- (1 - dPVtranche/(100*dPVindex) * K1adj)/(1-K1adj)
+ }else{
+ Kmod <- adjust.attachments(c(K1, K2), index$loss, index$factor)
+ dPVtranche <- BCtranche.pv(defaultprobplus, issuerweights, recov, cs, Kmod[1], Kmod[2], rho1, rho2,
+ Z, w, N)$bp -
+ BCtranche.pv(defaultprobminus, issuerweights, recov, cs, Kmod[1], Kmod[2], rho1, rho2,
+ Z, w, N)$bp
+ delta <- dPVtranche/(100*dPVindex)
+ }
+ ## dPVindex <- BCtranche.pv(portfolioplus, index, coupon, 0, 1, 0, 0.5, lu)$bp-
+ ## BCtranche.pv(portfoliominus, index, coupon, 0, 1, 0, 0.5, lu)$bp
+ return( delta )
+}
+
+BCstrikes <- function(portfolio, index, coupon, K, rho, N=101) {
+ ## computes the strikes as a percentage of expected loss
+ EL <- c()
+ for(i in 2:length(K)){
+ EL <- c(EL, -BCtranche.pv(portfolio, index, coupon, K[i-1], K[i], rho[i-1], rho[i], N)$pl)
+ }
+ Kmodified <- adjust.attachments(K, index$loss, index$factor)
+ return(cumsum(EL*diff(Kmodified))/sum(EL*diff(Kmodified)))
+}
+
+delta.factor <- function(K1, K2, index){
+ ## compute the factor to convert from delta on current notional to delta on original notional
+ ## K1 and K2 original strikes
+ factor <- (adjust.attachments(K2, index$loss, index$factor)
+ -adjust.attachments(K1, index$loss, index$factor))/(K2-K1)
+ return( factor )
+}
+
+MFupdate.prob <- function(Z, w, rho, defaultprob){
+ ## update the probabilites based on a non gaussian factor
+ ## distribution so that the pv of the cds stays the same.
+ p <- matrix(0, nrow(defaultprob), ncol(defaultprob))
+ for(i in 1:nrow(defaultprob)){
+ for(j in 1:ncol(defaultprob)){
+ p[i,j] <- fit.prob(Z, w, rho[i], defaultprob[i,j])
+ }
+ }
+ return( p )
+}
+
+MFupdate.probC <- function(Z, w, rho, defaultprob){
+ ## update the probabilities based on a non gaussian factor
+ ## distribution so that the pv of the cds stays the same.
+ p <- matrix(0, nrow(defaultprob), ncol(defaultprob))
+ for(i in 1:nrow(defaultprob)){
+ for(j in 1:ncol(defaultprob)){
+ p[i,j] <- .C("fitprob", as.double(Z), as.double(w), as.integer(length(Z)),
+ as.double(rho[i]), as.double(defaultprob[i,j]), q = double(1))$q
+ }
+ }
+ return( p )
+}
+
+MFlossrecovdist.prepay <- function(w, Z, rho, defaultprob, defaultprobmod, prepayprob, prepayprobmod,
+ issuerweights, recov, Ngrid=2*length(issuerweights)+1, defaultflag=FALSE){
+ ## computes the loss and recovery distribution using the modified factor distribution
+ n.credit <- length(issuerweights)
+ n.int <- length(w)
+ Rstoch <- array(0, dim=c(n.int, n.credit, ncol(defaultprob)))
+ for(t in 1:ncol(defaultprob)){
+ for(i in 1:n.credit){
+ Rstoch[,i,t] <- stochasticrecov(recov[i], 0, Z, w, rho, defaultprob[i,t], defaultprobmod[i,t])
+ }
+ }
+ parf <- function(i){
+ dpshocked <- apply(defaultprobmod, 2, shockprob, rho=rho, Z=Z[i])
+ ppshocked <- apply(prepayprobmod, 2, shockprob, rho=rho, Z=-Z[i])
+ S <- 1 - Rstoch[i,,]
+ dist <- lossrecovdist.term(dpshocked, ppshocked, issuerweights, S, Ngrid, defaultflag)
+ }
+ L <- matrix(0, Ngrid, ncol(defaultprob))
+ R <- matrix(0, Ngrid, ncol(defaultprob))
+ for(i in 1:length(w)){
+ dist <- parf(i)
+ L <- L + dist$L * w[i]
+ R <- R + dist$R * w[i]
+ }
+ return( list(L=L, R=R) )
+}
+
+MFlossdist.joint <- function(cl, w, Z, rho, defaultprob, defaultprobmod, issuerweights, recov,
+ Ngrid=2*length(issuerweights)+1, defaultflag=FALSE){
+ ## rowSums(Q) is the default/loss distribution depending if
+ ## defaultflag is TRUE or FALSE (default setting is FALSE)
+ ## colSums(Q) is the recovery distribution
+ ## so that recovery is the y axis and L/D is the x axis
+ ## if we use the persp function, losses is the axes facing us,
+ ## and R is the axis going away from us.
+ n.credit <- length(issuerweights)
+ n.int <- lenth(w)
+ Rstoch <- array(0, dim=c(n.int, n.credit, ncol(defaultprob)))
+ for(t in 1:ncol(defaultprob)){
+ for(i in 1:n.credit){
+ Rstoch[,i,t] <- stochasticrecov(recov[i], 0, Z, w, rho, defaultprob[i,t], defaultprobmod[i,t])
+ }
+ }
+ parf <- function(i){
+ pshocked <- apply(defaultprobmod, 2, shockprob, rho=rho, Z=Z[i])
+ S <- 1 - Rstoch[i,,]
+ dist <- lossrecovdist.joint.term(pshocked, 0, issuerweights, S, Ngrid, defaultflag)
+ gc()
+ return(dist)
+ }
+ temp <- parSapply(cl, 1:length(w), parf)
+ clusterCall(cl, gc)
+ Q <- array(0, dim=c(ncol(defaultprob), Ngrid, Ngrid))
+ for(i in 1:length(w)){
+ Q <- Q + w[i]*array(temp[,i], dim=c(ncol(defaultprob), Ngrid, Ngrid))
+ }
+ return( Q )
+}
+
+MFlossdist.prepay.joint <- function(w, Z, rho, defaultprob, defaultprobmod,
+ prepayprob, prepayprobmod, issuerweights, recov,
+ Ngrid=2*length(issuerweights)+1, defaultflag=FALSE){
+ ## rowSums is the loss distribution
+ ## colSums is the recovery distribution
+ ## so that recovery is the y axis and L is the x axis
+ ## if we use the persp function, losses is the axes facing us,
+ ## and R is the axis going away from us.
+ n.credit <- length(issuerweights)
+ n.int <- length(w)
+ Rstoch <- array(0, dim=c(n.credit, n.int, ncol(defaultprob)))
+
+ for(t in 1:ncol(defaultprob)){
+ for(i in 1:n.credit){
+ Rstoch[i,,t] <- stochasticrecovC(recov[i], 0, Z, w, rho[i],
+ defaultprob[i,t], defaultprobmod[i,t])
+ }
+ }
+
+ Q <- array(0, dim=c(ncol(defaultprob), Ngrid, Ngrid))
+ for(t in 1:ncol(defaultprob)){
+ S <- 1 - Rstoch[,,t]
+ Q[t,,] <- lossdistC.prepay.jointZ(defaultprobmod[,t], prepayprobmod[,t], issuerweights,
+ S, Ngrid, defaultflag, rho, Z, w)
+ }
+ return( Q )
+}
+
+MFtranche.pv <- function(cl, cs, w, rho, defaultprob, defaultprobmod, issuerweights, recov,
+ Kmodified, Ngrid=length(issuerweights)+1){
+ ## computes the tranches pv using the modified factor distribution
+ ## p is the modified probability so that
+ n.credit <- length(issuerweights)
+ Rstoch <- array(0, dim=c(n.int, n.credit, ncol(defaultprob)))
+ for(t in 1:ncol(defaultprob)){
+ for(i in 1:n.credit){
+ Rstoch[,i,t] <- stochasticrecov(recov[i], 0, Z, w, rho, defaultprob[i,t], defaultprobmod[i,t])
+ }
+ }
+ parf <- function(i){
+ pshocked <- apply(defaultprobmod, 2, shockprob, rho=rho, Z=Z[i])
+ S <- 1 - Rstoch[i,,]
+ dist <- lossrecovdist.term(pshocked, 0, issuerweights, S, Ngrid)
+ return( tranche.pvvec(Kmodified, dist$L, dist$R, cs))
+ }
+ clusterExport(cl, list("Rstoch", "p"), envir=environment())
+ result <- parSapply(cl, 1:length(w), parf)
+ return( list(pv=100*(1+result%*%w), pv.w=result))
+}
diff --git a/src/Makevars b/src/Makevars new file mode 100644 index 0000000..f6790ff --- /dev/null +++ b/src/Makevars @@ -0,0 +1,2 @@ +PKG_CFLAGS=$(SHLIB_OPENMP_CFLAGS)
+PKG_LIBS=$(SHLIB_OPENMP_CFLAGS)
diff --git a/src/Makevars.win b/src/Makevars.win new file mode 100644 index 0000000..6eb170c --- /dev/null +++ b/src/Makevars.win @@ -0,0 +1,2 @@ +PKG_CFLAGS=$(SHLIB_OPENMP_CFLAGS)
+PKG_LIBS=$(SHLIB_OPENMP_CFLAGS) -LOpenBLAS/lib -lopenblas
diff --git a/src/lossdistrib.c b/src/lossdistrib.c new file mode 100644 index 0000000..77ea335 --- /dev/null +++ b/src/lossdistrib.c @@ -0,0 +1,760 @@ +#include <R.h>
+#include <Rmath.h>
+#include <string.h>
+#include <omp.h>
+#include "lossdistrib.h"
+
+#define MIN(x, y) (((x) < (y)) ? (x) : (y))
+
+extern int dgemv_(char* trans, int *m, int *n, double* alpha, double* A, int* lda,
+ double* x, int* incx, double* beta, double* y, int* incy);
+extern double ddot_(int* n, double* dx, int* incx, double* dy, int* incy);
+extern int dscal_(int* n, double* da, double* dx, int* incx);
+extern int daxpy_(int* n, double* da, double* dx, int* incx, double* dy, int* incy);
+extern void openblas_set_num_threads(int);
+
+void lossdistrib(double *p, int *np, double *w, double *S, int *N, int *defaultflag,
+ double *q) {
+ /* recursive algorithm with first order correction for computing
+ the loss distribution.
+ p vector of default probabilities
+ np length of p
+ w issuer weights
+ S vector of severities (should be same length as p)
+ N number of ticks in the grid
+ defaultflag if true compute the default distribution
+ q the loss distribution */
+
+ int i, j, d1, d2, M;
+ double lu, d, p1, p2, sum;
+ double *qtemp;
+
+ lu = 1./(*N-1);
+ qtemp = calloc(*N, sizeof(double));
+ q[0] = 1;
+ M = 1;
+ for(i=0; i<(*np); i++){
+ d = (*defaultflag)? w[i]/lu : S[i] * w[i]/ lu;
+ d1 = floor(d);
+ d2 = ceil(d);
+ p1 = p[i] * (d2-d);
+ p2 = p[i] - p1;
+ memcpy(qtemp, q, MIN(M, *N) * sizeof(double));
+ for(j=0; j < MIN(M, *N); j++){
+ q[j] = (1-p[i]) * q[j];
+ }
+ for(j=0; j < MIN(M, *N-d2); j++){
+ q[d1+j] += p1 * qtemp[j];
+ q[d2+j] += p2 * qtemp[j];
+ };
+ M+=d2;
+ }
+
+ /* correction for weight loss */
+ if(M > *N){
+ sum = 0;
+ for(j=0; j<MIN(M, *N); j++){
+ sum += q[j];
+ }
+ q[*N-1] += 1-sum;
+ }
+ free(qtemp);
+}
+
+void lossdistrib_blas(double *p, int *np, double *w, double *S, int *N, int *defaultflag,
+ double *q) {
+ /* recursive algorithm with first order correction for computing
+ the loss distribution.
+ p: vector of default probabilities
+ np: length of p
+ w: issuer weights
+ S: vector of severities (should be same length as p)
+ N: number of ticks in the grid
+ defaultflag: if true compute the default distribution
+ q: the loss distribution */
+
+ int i, j, d1, d2, M;
+ double lu, d, p1, p2, sum;
+ double *qtemp;
+ int bound;
+ double pbar;
+ int one = 1;
+ openblas_set_num_threads(1);
+ lu = 1./(*N-1);
+ qtemp = calloc(*N, sizeof(double));
+ q[0] = 1;
+ M = 1;
+ for(i=0; i<(*np); i++){
+ d = (*defaultflag)? w[i]/lu : S[i] * w[i]/ lu;
+ d1 = floor(d);
+ d2 = ceil(d);
+ p1 = p[i] * (d2-d);
+ p2 = p[i] - p1;
+ memcpy(qtemp, q, MIN(M, *N) * sizeof(double));
+ pbar = 1-p[i];
+ bound = MIN(M, *N);
+ dscal_(&bound, &pbar, q, &one);
+ bound = MIN(M, *N-d2);
+ daxpy_(&bound, &p1, qtemp, &one, q+d1, &one);
+ daxpy_(&bound, &p2, qtemp, &one, q+d2, &one);
+ M += d2;
+ }
+ /* correction for weight loss */
+ if(M > *N){
+ sum = 0;
+ for(j=0; j<MIN(M, *N); j++){
+ sum += q[j];
+ }
+ q[*N-1] += 1-sum;
+ }
+ free(qtemp);
+}
+
+void lossdistrib_Z(double *p, int *np, double *w, double *S, int *N, int *defaultflag,
+ double *rho, double *Z, int *nZ, double *q){
+ int i, j;
+ double* pshocked = malloc(sizeof(double) * (*np) * (*nZ));
+
+ #pragma omp parallel for private(j)
+ for(i = 0; i < *nZ; i++){
+ for(j = 0; j < *np; j++){
+ pshocked[j + (*np) * i] = shockprob(p[j], rho[j], Z[i], 0);
+ }
+ lossdistrib_blas(pshocked + (*np) * i, np, w, S + (*np) * i, N,
+ defaultflag, q + (*N) * i);
+ }
+ free(pshocked);
+}
+
+void lossdistrib_truncated(double *p, int *np, double *w, double *S, int *N,
+ int *T, int *defaultflag, double *q) {
+ /* recursive algorithm with first order correction for computing
+ the loss distribution.
+ input:
+ p vector of default probabilities
+ np length of p
+ S vector of severities (should be same length as p)
+ N number of ticks in the grid
+ T where to truncate the distribution
+ defaultflag if true computes the default distribution
+ output:
+ q the loss distribution */
+
+ int i, j, d1, d2, M;
+ double lu, d, p1, p2;
+ double *q1, *q2;
+
+ lu = 1./(*N-1);
+ q1 = calloc( *T, sizeof(double));
+ q2 = calloc( *T, sizeof(double));
+ q[0] = 1;
+ M = 1;
+ for(i=0; i<(*np); i++){
+ d = (*defaultflag)? w[i] / lu : S[i] * w[i] / lu;
+ d1 = floor(d);
+ d2 = ceil(d);
+ p1 = p[i] * (d2-d);
+ p2 = p[i] - p1;
+ for(j=0; j < MIN(M, *T); j++){
+ q1[j] = p1 * q[j];
+ q2[j] = p2 * q[j];
+ q[j] = (1-p[i]) * q[j];
+ }
+ for(j=0; j < MIN(M, *T-d1); j++){
+ q[d1+j] += q1[j];
+ };
+ for(j=0; j < MIN(M, *T-d2); j++){
+ q[d2+j] += q2[j];
+ };
+ M += d2;
+ }
+ free(q1);
+ free(q2);
+}
+
+void lossdistrib_joint(double *p, int *np, double *w, double *S, int *N, int *defaultflag, double *q) {
+ /* recursive algorithm with first order correction
+ computes jointly the loss and recovery distribution
+ p vector of default probabilities
+ np length of p
+ w vector of issuer weights (length np)
+ S vector of severities (should be same length as p)
+ N number of ticks in the grid
+ defaultflag if true computes the default distribution
+ q the joint probability distribution */
+
+ int i, j, k, m, n;
+ int Mx, My;
+ double lu, x, y, sum;
+ double alpha1, alpha2, beta1, beta2;
+ double w1, w2, w3, w4;
+ double *qtemp;
+
+ lu = 1./(*N-1);
+ qtemp = calloc( (*N) * (*N), sizeof(double));
+ q[0] = 1;
+ Mx=1;
+ My=1;
+ for(k=0; k<(*np); k++){
+ x = (*defaultflag)? w[k] /lu : S[k] * w[k] / lu;
+ y = (1-S[k]) * w[k] / lu;
+ i = floor(x);
+ j = floor(y);
+ alpha1 = i + 1 - x;
+ alpha2 = 1 - alpha1;
+ beta1 = j + 1 - y;
+ beta2 = 1 - beta1;
+ w1 = alpha1 * beta1;
+ w2 = alpha1 * beta2;
+ w3 = alpha2 * beta2;
+ w4 = alpha2 * beta1;
+
+ for(n=0; n<MIN(My, *N); n++){
+ memcpy(qtemp+n*(*N), q+n*(*N), MIN(Mx, *N) * sizeof(double));
+ }
+ for(n=0; n<MIN(My, *N); n++){
+ for(m=0; m<MIN(Mx, *N); m++){
+ q[m+(*N)*n] = (1-p[k])* q[m+(*N)*n];
+ }
+ }
+ for(n=0; n < MIN(My, *N-j-1); n++){
+ for(m=0; m < MIN(Mx, *N-i-1); m++){
+ q[i+m+(*N)*(j+n)] += w1 * p[k] * qtemp[m+(*N)*n];
+ q[i+m+(*N)*(j+1+n)] += w2 * p[k] * qtemp[m+(*N)*n];
+ q[i+1+m+(*N)*(j+1+n)] += w3 * p[k] * qtemp[m+(*N)*n];
+ q[i+1+m+(*N)*(j+n)] += w4 * p[k] *qtemp[m+(*N)*n];
+ }
+ }
+ Mx += i+1;
+ My += j+1;
+ }
+ /* correction for weight loss */
+ if(Mx>*N || My>*N){
+ sum = 0;
+ for(m=0; m < MIN(Mx, *N); m++){
+ for(n=0; n < MIN(My, *N); n++){
+ sum += q[m+n*(*N)];
+ }
+ }
+ q[MIN(*N, Mx)*MIN(My,*N)-1] += 1 - sum;
+ }
+ free(qtemp);
+}
+
+void lossdistrib_joint_blas(double *p, int *np, double *w, double *S, int *N, int *defaultflag, double *q) {
+ /* recursive algorithm with first order correction
+ computes jointly the loss and recovery distribution
+ p vector of default probabilities
+ np length of p
+ w vector of issuer weights (length np)
+ S vector of severities (should be same length as p)
+ N number of ticks in the grid
+ defaultflag if true computes the default distribution
+ q the joint probability distribution */
+
+ int i, j, k, m, n;
+ int Mx, My;
+ double lu, x, y, sum, pbar;
+ double alpha1, alpha2, beta1, beta2;
+ double w1, w2, w3, w4;
+ double *qtemp;
+ int bound;
+ int one = 1;
+
+ /* only use one thread, performance is horrible if use multiple threads */
+ openblas_set_num_threads(1);
+
+ lu = 1./(*N-1);
+ qtemp = calloc( (*N) * (*N), sizeof(double));
+ q[0] = 1;
+ Mx=1;
+ My=1;
+ for(k=0; k<(*np); k++){
+ x = (*defaultflag)? w[k] /lu : S[k] * w[k] / lu;
+ y = (1-S[k]) * w[k] / lu;
+ i = floor(x);
+ j = floor(y);
+ alpha1 = i + 1 - x;
+ alpha2 = 1 - alpha1;
+ beta1 = j + 1 - y;
+ beta2 = 1 - beta1;
+ w1 = alpha1 * beta1 * p[k];
+ w2 = alpha1 * beta2 * p[k];
+ w3 = alpha2 * beta2 * p[k];
+ w4 = alpha2 * beta1 * p[k];
+
+ for(n=0; n<MIN(My, *N); n++){
+ memcpy(qtemp+n*(*N), q+n*(*N), MIN(Mx, *N) * sizeof(double));
+ }
+
+ bound = MIN(Mx, *N);
+ pbar = 1-p[k];
+ for(n=0; n<MIN(My, *N); n++){
+ dscal_(&bound, &pbar, q+(*N)*n, &one);
+ }
+ bound = MIN(Mx, *N-i-1);
+ for(n=0; n < MIN(My, *N-j-1); n++){
+ daxpy_(&bound, &w1, qtemp+(*N)*n, &one, q+i+(*N)*(j+n), &one);
+ daxpy_(&bound, &w2, qtemp+(*N)*n, &one, q+i+(*N)*(j+1+n), &one);
+ daxpy_(&bound, &w3, qtemp+(*N)*n, &one, q+i+1+(*N)*(j+1+n), &one);
+ daxpy_(&bound, &w4, qtemp+(*N)*n, &one, q+i+1+(*N)*(j+n), &one);
+ }
+ Mx += i+1;
+ My += j+1;
+ }
+ /* correction for weight loss */
+ if(Mx>*N || My>*N){
+ sum = 0;
+ for(m=0; m < MIN(Mx, *N); m++){
+ for(n=0; n < MIN(My, *N); n++){
+ sum += q[m+n*(*N)];
+ }
+ }
+ q[MIN(*N, Mx)*MIN(My,*N)-1] += 1 - sum;
+ }
+ free(qtemp);
+}
+
+void recovdist(double *dp, double *pp, int *n, double *w, double *S, int *N, double *q) {
+ /* recursive algorithm with first order correction for computing
+ the recovery distribution in case of prepayment.
+ dp vector of default probabilities
+ pp vector of prepay probabilities
+ n length of p
+ S vector of severities (should be same length as p)
+ w vector of weights
+ N number of ticks in the grid
+ q the loss distribution */
+
+ int i, j, d1l, d1u, d2l, d2u;
+ int M;
+ double lu, d1, d2, dp1, dp2, pp1, pp2, sum;
+ double *qtemp;
+
+ lu = 1./(*N - 1);
+ qtemp = calloc( (*N), sizeof(double));
+ q[0] = 1;
+ M=1;
+ for(i=0; i<(*n); i++){
+ d1 = w[i] * (1-S[i]) /lu;
+ d2 = w[i]/lu;
+ d1l = floor(d1);
+ d1u = d1l + 1;
+ d2l = floor(d2);
+ d2u = d2l + 1;
+ dp1 = dp[i] * (d1u - d1);
+ dp2 = dp[i] - dp1;
+ pp1 = pp[i] * (d2u - d2);
+ pp2 = pp[i] - pp1;
+ memcpy(qtemp, q, MIN(M, *N) * sizeof(double));
+ for(j = 0; j< MIN(M, *N); j++){
+ q[j] = (1-dp[i]-pp[i]) * q[j];
+ }
+ for(j=0; j < MIN(M, *N-d2u); j++){
+ q[d1l+j] += dp1 * qtemp[j];
+ q[d1u+j] += dp2 * qtemp[j];
+ q[d2l+j] += pp1 * qtemp[j];
+ q[d2u+j] += pp2 * qtemp[j];
+ };
+ M += d2u;
+ }
+ /* correction for weight loss */
+ if(M>*N){
+ sum = 0;
+ for(j=0; j<MIN(M, *N); j++){
+ sum += q[j];
+ }
+ q[*N-1] += 1-sum;
+ }
+ free(qtemp);
+}
+
+void lossdistrib_prepay_joint(double *dp, double *pp, int *ndp, double *w,
+ double *S, int *N, int *defaultflag, double *q) {
+ int i, j1, j2, k, m, n;
+ double lu, x, y1, y2, sum;
+ double alpha1, alpha2, beta1, beta2;
+ double dpw1, dpw2, dpw3, dpw4;
+ double ppw1, ppw2, ppw3;
+ double *qtemp;
+ int Mx, My;
+
+ lu = 1./(*N-1);
+ qtemp = calloc((*N) * (*N), sizeof(double));
+ q[0] = 1;
+ Mx=1;
+ My=1;
+
+ for(k=0; k<(*ndp); k++){
+ y1 = (1-S[k]) * w[k]/lu;
+ y2 = w[k]/lu;
+ x = (*defaultflag)? y2: y2-y1;
+ i = floor(x);
+ j1 = floor(y1);
+ j2 = floor(y2);
+ alpha1 = i + 1 - x;
+ alpha2 = 1 - alpha1;
+ beta1 = j1 + 1 - y1;
+ beta2 = 1 - beta1;
+ dpw1 = alpha1 * beta1 * dp[k];
+ dpw2 = alpha1 * beta2 * dp[k];
+ dpw3 = alpha2 * beta2 * dp[k];
+ dpw4 = alpha2 * beta1 * dp[k];
+
+ /* by default distribution, we mean names fractions of names that disappeared
+ either because of default or prepayment */
+ for(n=0; n<MIN(My, *N); n++){
+ memcpy(qtemp+n*(*N), q+n*(*N), MIN(Mx, *N) * sizeof(double));
+ }
+ for(n=0; n<MIN(My, *N); n++){
+ for(m=0; m<MIN(Mx, *N); m++){
+ q[m+(*N)*n] = (1-dp[k]-pp[k]) * q[m+(*N)*n];
+ }
+ }
+ if(*defaultflag){
+ ppw1 = alpha1 * alpha1 * pp[k];
+ ppw2 = alpha1 * alpha2 * pp[k];
+ ppw3 = alpha2 * alpha2 * pp[k];
+ for(n=0; n < MIN(My, *N-j2-1); n++){
+ for(m=0; m < MIN(Mx, *N-i-1); m++){
+ q[i+m+(*N)*(j1+n)] += dpw1 * qtemp[m+(*N)*n];
+ q[i+m+(*N)*(j1+1+n)] += dpw2 * qtemp[m+(*N)*n];
+ q[i+1+m+(*N)*(j1+1+n)] += dpw3 * qtemp[m+(*N)*n];
+ q[i+1+m+(*N)*(j1+n)] += dpw4 * qtemp[m+(*N)*n];
+
+ q[i+m+(*N)*(j2+n)] += ppw1 * qtemp[m+(*N)*n];
+ q[i+m+(*N)*(j2+1+n)] += ppw2 * qtemp[m+(*N)*n];
+ q[i+1+m+(*N)*(j2+1+n)] += ppw3 * qtemp[m+(*N)*n];
+ q[i+1+m+(*N)*(j2+n)] += ppw2 * qtemp[m+(*N)*n];
+ }
+ }
+ }else{
+ for(n=0; n < MIN(My, *N-j2-1); n++){
+ for(m=0; m < MIN(Mx, *N-i-1); m++){
+ q[i+m+(*N)*(j1+n)] += dpw1 * qtemp[m+(*N)*n];
+ q[i+m+(*N)*(j1+1+n)] += dpw2 * qtemp[m+(*N)*n];
+ q[i+1+m+(*N)*(j1+1+n)] += dpw3 * qtemp[m+(*N)*n];
+ q[i+1+m+(*N)*(j1+n)] += dpw4 * qtemp[m+(*N)*n];
+ q[m+(*N)*(j2+n)] += pp[k]*(j2+1-y2) * qtemp[m+(*N)*n];
+ q[m+(*N)*(j2+1+n)] += pp[k]*(y2-j2) * qtemp[m+(*N)*n];
+ }
+ }
+ }
+ Mx += i + 1;
+ My += j2 + 1;
+ }
+ /* correction for weight loss */
+ if(Mx>*N || My>*N){
+ sum = 0;
+ for(m=0; m < MIN(Mx, *N); m++){
+ for(n=0; n < MIN(My, *N); n++){
+ sum += q[m+n*(*N)];
+ }
+ }
+ q[MIN(*N, Mx)*MIN(My,*N)-1] += 1 - sum;
+ }
+ free(qtemp);
+}
+
+void lossdistrib_prepay_joint_blas(double *dp, double *pp, int *ndp, double *w,
+ double *S, int *N, int *defaultflag, double *q) {
+ int i, j1, j2, k, m, n;
+ double lu, x, y1, y2, sum;
+ double alpha1, alpha2, beta1, beta2;
+ double dpw1, dpw2, dpw3, dpw4;
+ double ppw1, ppw2, ppw3;
+ double *qtemp;
+ int Mx, My, bound;
+ double pbar;
+ int one = 1;
+
+ lu = 1./(*N-1);
+ qtemp = calloc((*N) * (*N), sizeof(double));
+ q[0] = 1;
+ Mx=1;
+ My=1;
+
+ /* only use one thread, performance is horrible if use multiple threads */
+ openblas_set_num_threads(1);
+ for(k=0; k<(*ndp); k++){
+ y1 = (1-S[k]) * w[k]/lu;
+ y2 = w[k]/lu;
+ x = (*defaultflag)? y2: y2-y1;
+ i = floor(x);
+ j1 = floor(y1);
+ j2 = floor(y2);
+ alpha1 = i + 1 - x;
+ alpha2 = 1 - alpha1;
+ beta1 = j1 + 1 - y1;
+ beta2 = 1 - beta1;
+ dpw1 = alpha1 * beta1 * dp[k];
+ dpw2 = alpha1 * beta2 * dp[k];
+ dpw3 = alpha2 * beta2 * dp[k];
+ dpw4 = alpha2 * beta1 * dp[k];
+
+ /* by default distribution, we mean names fractions of names that disappeared
+ either because of default or prepayment */
+ for(n=0; n<MIN(My, *N); n++){
+ memcpy(qtemp+n*(*N), q+n*(*N), MIN(Mx, *N) * sizeof(double));
+ }
+ bound = MIN(Mx, *N);
+ pbar = 1-dp[k]-pp[k];
+ for(n=0; n<MIN(My, *N); n++){
+ dscal_(&bound, &pbar, q+(*N)*n, &one);
+ }
+ bound = MIN(Mx, *N-i-1);
+ if(*defaultflag){
+ ppw1 = alpha1 * alpha1 * pp[k];
+ ppw2 = alpha1 * alpha2 * pp[k];
+ ppw3 = alpha2 * alpha2 * pp[k];
+ for(n=0; n < MIN(My, *N-j2-1); n++){
+ daxpy_(&bound, &dpw1, qtemp+(*N)*n, &one, q+i+(*N)*(j1+n), &one);
+ daxpy_(&bound, &dpw2, qtemp+(*N)*n, &one, q+i+(*N)*(j1+1+n), &one);
+ daxpy_(&bound, &dpw3, qtemp+(*N)*n, &one, q+i+1+(*N)*(j1+1+n), &one);
+ daxpy_(&bound, &dpw4, qtemp+(*N)*n, &one, q+i+1+(*N)*(j1+n), &one);
+
+ daxpy_(&bound, &ppw1, qtemp+(*N)*n, &one, q+i+(*N)*(j2+n), &one);
+ daxpy_(&bound, &ppw2, qtemp+(*N)*n, &one, q+i+(*N)*(j2+1+n), &one);
+ daxpy_(&bound, &ppw3, qtemp+(*N)*n, &one, q+i+1+(*N)*(j2+1+n), &one);
+ daxpy_(&bound, &ppw2, qtemp+(*N)*n, &one, q+i+1+(*N)*(j2+n), &one);
+ }
+ }else{
+ ppw1 = pp[k] * (j2+1-y2);
+ ppw2 = pp[k] * (y2-j2);
+ for(n=0; n < MIN(My, *N-j2-1); n++){
+ daxpy_(&bound, &dpw1, qtemp+(*N)*n, &one, q+i+(*N)*(j1+n), &one);
+ daxpy_(&bound, &dpw2, qtemp+(*N)*n, &one, q+i+(*N)*(j1+1+n), &one);
+ daxpy_(&bound, &dpw3, qtemp+(*N)*n, &one, q+i+1+(*N)*(j1+1+n), &one);
+ daxpy_(&bound, &dpw4, qtemp+(*N)*n, &one, q+i+1+(*N)*(j1+n), &one);
+ daxpy_(&bound, &ppw1, qtemp+(*N)*n, &one, q+(*N)*(j2+n), &one);
+ daxpy_(&bound, &ppw2, qtemp+(*N)*n, &one, q+(*N)*(j2+1+n), &one);
+ }
+ }
+ Mx += i + 1;
+ My += j2 + 1;
+ }
+ /* correction for weight loss */
+ if(Mx>*N || My>*N){
+ sum = 0;
+ for(m=0; m < MIN(Mx, *N); m++){
+ for(n=0; n < MIN(My, *N); n++){
+ sum += q[m+n*(*N)];
+ }
+ }
+ q[MIN(*N, Mx)*MIN(My,*N)-1] += 1 - sum;
+ }
+ free(qtemp);
+}
+
+double shockprob(double p, double rho, double Z, int give_log){
+ if(rho==1){
+ return((double)(Z<=qnorm(p, 0, 1, 1, 0)));
+ }else{
+ return( pnorm( (qnorm(p, 0, 1, 1, 0) - sqrt(rho) * Z)/sqrt(1 - rho), 0, 1, 1, give_log));
+ }
+}
+
+double dqnorm(double x){
+ return 1/dnorm(qnorm(x, 0, 1, 1, 0), 0, 1, 0);
+}
+
+double dshockprob(double p, double rho, double Z){
+ return( dnorm((qnorm(p, 0, 1, 1, 0) - sqrt(rho) * Z)/sqrt(1-rho), 0, 1, 0) * dqnorm(p)/sqrt(1-rho) );
+}
+
+void shockprobvec2(double p, double rho, double* Z, int nZ, double *q){
+ /* return a two column vectors with shockprob in the first column
+ and dshockprob in the second column*/
+ int i;
+ #pragma omp parallel for
+ for(i = 0; i < nZ; i++){
+ q[i] = shockprob(p, rho, Z[i], 0);
+ q[i + nZ] = dshockprob(p, rho, Z[i]);
+ }
+}
+
+double shockseverity(double S, double Z, double rho, double p){
+ if(p==0){
+ return 0;
+ }else{
+ return( exp(shockprob(S * p, rho, Z, 1) - shockprob(p, rho, Z, 1)) );
+ }
+}
+
+double quantile(double* Z, double* w, int nZ, double p0){
+ double cumw;
+ int i;
+ cumw = 0;
+ for(i=0; i<nZ; i++){
+ cumw += w[i];
+ if(cumw > p0){
+ break;
+ }
+ }
+ return( Z[i] );
+}
+
+void fitprob(double* Z, double* w, int* nZ, double* rho, double* p0, double* result){
+ double eps = 1e-12;
+ int one = 1;
+ double *q = malloc( 2 * (*nZ) * sizeof(double));
+ double dp, p, phi;
+
+ if(*p0 == 0){
+ *result = 0;
+ }else if(*rho == 1){
+ *result = pnorm(quantile(Z, w, *nZ, *p0), 0, 1, 1, 0);
+ }else{
+ shockprobvec2(*p0, *rho, Z, *nZ, q);
+ dp = (ddot_(nZ, q, &one, w, &one) - *p0)/ddot_(nZ, q + *nZ, &one, w, &one);
+ p = *p0;
+ while(fabs(dp) > eps){
+ phi = 1;
+ while( (p - phi * dp) < 0 || (p - phi * dp) > 1){
+ phi *= 0.8;
+ }
+ p -= phi * dp;
+ shockprobvec2(p, *rho, Z, *nZ, q);
+ dp = (ddot_(nZ, q, &one, w, &one) - *p0)/ddot_(nZ, q + *nZ, &one, w, &one);
+ }
+ *result = p;
+ }
+ free(q);
+}
+
+void stochasticrecov(double* R, double* Rtilde, double* Z, double* w, int* nZ,
+ double* rho, double* porig, double* pmod, double* q){
+ double ptemp, ptilde;
+ int i;
+ if(*porig==0){
+ for(i = 0; i < *nZ; i++){
+ q[i] = *R;
+ }
+ }else{
+ ptemp = (1 - *R) / (1 - *Rtilde) * *porig;
+ fitprob(Z, w, nZ, rho, &ptemp, &ptilde);
+ #pragma omp parallel for
+ for(i = 0; i < *nZ; i++){
+ q[i] = fabs(1 - (1 - *Rtilde) * exp( shockprob(ptilde, *rho, Z[i], 1) -
+ shockprob(*pmod, *rho, Z[i], 1)));
+ }
+ }
+}
+
+void lossdistrib_prepay_joint_Z(double *dp, double *pp, int *ndp, double *w,
+ double *S, int *N, int *defaultflag, double *rho,
+ double *Z, double *wZ, int *nZ, double *q) {
+ int i, j;
+ double* dpshocked = malloc(sizeof(double) * (*ndp) * (*nZ));
+ double* ppshocked = malloc(sizeof(double) * (*ndp) * (*nZ));
+ int N2 = (*N) * (*N);
+ double* qmat = malloc(sizeof(double) * N2 * (*nZ));
+
+ double alpha = 1;
+ double beta = 0;
+ int one = 1;
+
+#pragma omp parallel for private(j)
+ for(i = 0; i < *nZ; i++){
+ for(j = 0; j < *ndp; j++){
+ dpshocked[j + (*ndp) * i] = shockprob(dp[j], rho[j], Z[i], 0);
+ ppshocked[j + (*ndp) * i] = shockprob(pp[j], rho[j], -Z[i], 0);
+ }
+ lossdistrib_prepay_joint_blas(dpshocked + (*ndp) * i, ppshocked + (*ndp) * i, ndp,
+ w, S + (*ndp) * i, N, defaultflag, qmat + N2 * i);
+ }
+
+ dgemv_("n", &N2, nZ, &alpha, qmat, &N2, wZ, &one, &beta, q, &one);
+
+ free(dpshocked);
+ free(ppshocked);
+ free(qmat);
+}
+
+void lossdistrib_joint_Z(double *dp, int *ndp, double *w,
+ double *S, int *N, int *defaultflag, double *rho,
+ double *Z, double *wZ, int *nZ, double *q) {
+ int i, j;
+ double* dpshocked = malloc(sizeof(double) * (*ndp) * (*nZ));
+ int N2 = (*N) * (*N);
+ double* qmat = malloc(sizeof(double) * N2 * (*nZ));
+
+ double alpha = 1;
+ double beta = 0;
+ int one = 1;
+
+#pragma omp parallel for private(j)
+ for(i = 0; i < *nZ; i++){
+ for(j = 0; j < *ndp; j++){
+ dpshocked[j + (*ndp) * i] = shockprob(dp[j], rho[j], Z[i], 0);
+ }
+ lossdistrib_joint_blas(dpshocked + (*ndp) * i, ndp, w, S + (*ndp) * i, N,
+ defaultflag, qmat + N2 * i);
+ }
+
+ dgemv_("n", &N2, nZ, &alpha, qmat, &N2, wZ, &one, &beta, q, &one);
+
+ free(dpshocked);
+ free(qmat);
+}
+
+void BClossdist(double *defaultprob, int *dim1, int *dim2,
+ double *issuerweights, double *recov, double *Z, double *w,
+ int *n, double *rho, int *N, int *defaultflag,
+ double *L, double *R) {
+ /*
+ computes the loss and recovery distribution over time with a flat gaussian
+ correlation
+ inputs:
+ defaultprob: matrix of size dim1 x dim2. dim1 is the number of issuers
+ and dim2 number of time steps
+ issuerweights: vector of issuer weights (length dim1)
+ recov: vector of recoveries (length dim1)
+ Z: vector of factor values (length n)
+ w: vector of factor weights (length n)
+ rho: correlation beta vector (length dim1)
+ N: number of ticks in the grid
+ defaultflag: if true, computes the default distribution
+ outputs:
+ L: matrix of size (N, dim2)
+ R: matrix of size (N, dim2)
+ */
+ int t, i, j;
+ double g;
+ double *gshocked, *Rshocked, *Sshocked, *Lw, *Rw;
+ int one = 1;
+ double alpha = 1;
+ double beta = 0;
+
+ gshocked = malloc((*dim1) * (*n) * sizeof(double));
+ Rshocked = malloc((*dim1) * (*n) * sizeof(double));
+ Sshocked = malloc((*dim1) * (*n) * sizeof(double));
+ Lw = malloc((*N) * (*n) * sizeof(double));
+ Rw = malloc((*N) * (*n) * sizeof(double));
+
+
+ for(t=0; t < (*dim2); t++) {
+ memset(Lw, 0, (*N) * (*n) * sizeof(double));
+ memset(Rw, 0, (*N) * (*n) * sizeof(double));
+ #pragma omp parallel for private(j, g)
+ for(i=0; i < *n; i++){
+ for(j=0; j < (*dim1); j++){
+ g = defaultprob[j + (*dim1) * t];
+ gshocked[j+(*dim1)*i] = shockprob(g, rho[j], Z[i], 0);
+ Sshocked[j+(*dim1)*i] = shockseverity(1-recov[j], Z[i], rho[j], g);
+ Rshocked[j+(*dim1)*i] = 1 - Sshocked[j+(*dim1)*i];
+ }
+ lossdistrib_blas(gshocked + (*dim1) * i, dim1, issuerweights, Sshocked + (*dim1)*i, N, defaultflag,
+ Lw + i * (*N));
+ lossdistrib_blas(gshocked + (*dim1) * i, dim1, issuerweights, Rshocked + (*dim1)*i, N, defaultflag,
+ Rw + i * (*N));
+ }
+ dgemv_("n", N, n, &alpha, Lw, N, w, &one, &beta, L + t * (*N), &one);
+ dgemv_("n", N, n, &alpha, Rw, N, w, &one, &beta, R + t * (*N), &one);
+ }
+ free(gshocked);
+ free(Rshocked);
+ free(Sshocked);
+ free(Lw);
+ free(Rw);
+}
diff --git a/src/lossdistrib.h b/src/lossdistrib.h new file mode 100644 index 0000000..d4bd974 --- /dev/null +++ b/src/lossdistrib.h @@ -0,0 +1,46 @@ +void lossdistrib(double *p, int *np, double *w, double *S, int *N, int *defaultflag, double *q);
+void lossdistrib_blas(double *p, int *np, double *w, double *S, int *N, int *defaultflag, double *q);
+
+double shockprob(double p, double rho, double Z, int give_log);
+
+void lossdistrib_Z(double *p, int *np, double *w, double *S, int *N, int *defaultflag,
+ double *rho, double *Z, int *nZ, double *q);
+
+void lossdistrib_truncated(double *p, int *np, double *w, double *S, int *N,
+ int *T, int *defaultflag, double *q);
+
+void lossdistrib_joint(double *p, int *np, double *w, double *S, int *N,
+ int *defaultflag, double *q);
+
+void lossdistrib_joint_blas(double *p, int *np, double *w, double *S, int *N,
+ int *defaultflag, double *q);
+
+void recovdist(double *dp, double *pp, int *n, double *w, double *S, int *N, double *q);
+
+void lossdistrib_prepay_joint(double *dp, double *pp, int *ndp, double *w,
+ double *S, int *N, int *defaultflag, double *q);
+double dqnorm(double x);
+
+double dshockprob(double p, double rho, double Z);
+
+void shockprobvec2(double p, double rho, double* Z, int nZ, double *q);
+
+double shockseverity(double S, double Z, double rho, double p);
+
+void fitprob(double* Z, double* w, int* nZ, double* rho, double* p0, double* result);
+
+void stochasticrecov(double* R, double* Rtilde, double* Z, double* w, int* nZ,
+ double* rho, double* porig, double* pmod, double* q);
+
+void lossdistrib_prepay_joint_Z(double *dp, double *pp, int *ndp, double *w,
+ double *S, int *N, int *defaultflag, double *rho,
+ double *Z, double *wZ, int *nZ, double *q);
+void lossdistrib_joint_Z(double *dp, int *ndp, double *w,
+ double *S, int *N, int *defaultflag, double *rho,
+ double *Z, double *wZ, int *nZ, double *q);
+
+void BClossdist(double *SurvProb, int *dim1, int *dim2, double *issuerweights,
+ double *recov, double *Z, double *w, int *n, double *rho, int *N,
+ int *defaultflag, double *L, double *R);
+
+double quantile(double* Z, double* w, int nZ, double p0);
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